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New Journal of Physics

Theory of incoherent self-phase modulation of non-stationary pulses

Solange Bessa Cavalcanti

Published Mar 27, 2002• 9 citations
Publisher

Abstract

A theory describing propagation of partially coherent pulse trains in Kerr media is proposed. It is shown that changes in the statistical properties of chaotic modulated pulses propagating under self-phase modulation (SPM) are easily obtained within the framework of cyclostationary processes. Specific applications for laser light and thermal light are considered showing that in contrast with laser light, the thermal light spectrum on propagation suffers a significant change which smears out the characteristic peaks of the SPM spectrum.

DOI
10.1088/1367-2630/4/1/319

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•Jan 18, 2016•0 citations
A theory describing propagation of partially coherent pulse trains in Kerr media is proposed. It is shown that changes in the statistical properties of chaotic modulated pulses propagating under self-phase modulation (SPM) are easily obtained within the framework of cyclostationary processes. Specific applications for laser light and thermal light are considered showing that in contrast with laser light, the thermal light spectrum on propagation suffers a significant change which smears out the characteristic peaks of the SPM spectrum.
We investigate the changes in the frequency spectrum of a partially coherent pulse brought on by a Kerr nonlinearity and by multiphoton ionization in a gas. We find that fluctuations in the parameters of the laser light cause the average spectrum of a pulse in a medium with a Kerr nonlinearity to be symmetric, with a single maximum at the center frequency. In the case of free-carrier generation, a long wing forms in the average spectrum that extends into the anti-Stokes region. We show that the ionization-induced nonlinearity gives rise to two time scales in the correlation function of the light.
We develop a travelling-wave formulation of the theory of quantum optics and apply it to the description of the self-phase modulation of a short coherent pulse of light. The infinite nonlinear phase shift that is produced by the vacuum fluctuations is treated, within our approach, through a renormalization procedure. The renormalized theory successfully describes the nonlinear chirp that the pulse undergoes in the course of its propagation and permits the calculation of the squeezing characteristics of self-phase modulation.
The consistent quantum theory of self-phase modulation (SPM) and cross-phase modulation (XPM) for ultrashort light pulses (USP) in medium with electronic Kerr-nonlinearity are developed. The approach makes use of momentum operator of electrical field which takes account of the inertial behaviour of the nonlinearity. The spectrum of quantum fluctuations of squeezed-quadrature component as a function of response time of nonlinearity and values of nonlinear phase shifts due to the SPM and XPM effects, is investigated.
Optical experiments reveal the fact that real laser pulses have random fluctuations in their amplitude and phase that crucially affect pulse evolution. Statistical optics considers the random nature of light to give a more realistic description of laser pulses behavior. Generation of ultrashort pulses, operating at frequencies close to internal transition frequencies of medium atoms, motivated the growing interest in studying on-resonance light-matter interactions. Moreover, there exist optical phenomena that only occur at optical resonance. Thus, near resonance light-matter interactions are of great importance. In this dissertation, statistical properties of ultrashort pulses propagating in different linear and nonlinear media near optical resonance is studied. Various partially coherent pulses are simulated and effects of initial statistical properties of pulses on their propagation in resonant absorbing and amplifying media are explored. The research performed throughout this thesis leads to following results. 1- Various classes of ultrashort self-similar partially coherent pulses are explored along with closed form expressions for their correlation functions. Also, the evolution of coherence properties of pulses upon their short-distance and long-distance propagation is investigated. 2- Generic partially coherent pulses are simulated and their global and local correlation properties upon propagation in resonant linear absorber media are studied. The evolution of the coherence functions of pulses shows that partially coherent pulses are strongly affected by the medium regarding to their coherence levels. A correlation area theorem is also derived to describe global correlation properties of stochastic pulses propagating in such media. 3- Evolution of small-area pulse coherence properties, propagating in linear amplifiers near optical resonance, is studied. Our simulation results reveal that more coherent pulses are amplified more effectively by the medium than are their less coherent counterparts. 4- Propagation of partially coherent pulses in resonant, inhomogenously broadened nonlinear media is simulated. Stochastic pulses of different coherence levels are generated to investigate effects of initial properties of pulses on their long-term evolution. We also provide evidence of self-induced transparency phenomena and soliton formation for relatively coherent pulses. Also, evolution of the coherence functions reveal that low-coherence pulses lose their coherence level upon propagation faster than do highly coherent pulses.